Three-body correlations in the variational wave function of liquidHe4

A product of two-body ($f_{\mathrm{ij}}$) and three-body ($f_{\mathrm{ijk}}$) correlation functions is used as a variational wave function for liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. The $f_{\mathrm{ijk}}$ take into account the backflows produced by two particles recoiling from each other. The distribution functions, the energy, and its uncertainty are all calculated using the Lennard-Jones-deBoer-Michel potential, and diagrammatic hypernetted-chain summation methods. The calculated equilibrium energy of -6.72 (±0.2)°K, is significantly lower than the -5.9°K obtained with only a product of $f_{\mathrm{ij}}$, and agrees with the -6.84°K estimated from a Monte Carlo integration of the many-body Schrödinger equation. The proposed wave function is simple enough to be useful in Fermi liquids.